Estimation in populations with rare events

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Abstract

Survey sampling is one of the most practiced subjects in statistics, with various methods having been proposed to estimate rare population parameters. Among these existing methods, not much attention has previously been focused on the estimation of parameters of rare sub-populations arising from a population which has a very skewed distribution. This is the primary motivation for this thesis, which involves sampling from a population which is composed of a mixture of a point mass at zero (‘good’ accounts) and a highly skewed non-zero distribution (‘bad’ accounts) in order to estimate the total bad dollar population.
We use simulation to obtain empirical results, such as mean, bias, and standard errors for six estimators. 2000 simulations are run for each of the 162 combinations of estimator (6), bad-dollar scenario (3), sample size (3), and sample allocation procedure (3). Based on these results, recommendations are made for optimal sampling strategy.